Group decision-making: Head-count versus intensity of preference

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Abstract

This paper puts forth a framework for reshaping the group decision-making process. The proposed framework extends from the usual one-issue-at-a-time decision-making to one that involves several related issues simultaneously. Weaknesses of the traditional majority voting mechanism are first identified, and then a different voting method that takes each individual voter's sentiment into account is discussed. Specifically, a decision-maker is asked to express his/her intensity of preference for the issues encountered. Three hierarchical structures—benefits, costs, and risks—are developed to evaluate the alternatives. Due to the nature of pairwise comparisons and synthesis, the proposed method is amenable to consensus building and has higher reliability and consistency. It can be used for candidate selection, e.g. governmental election, when a large population is involved. It is also effective for resource allocation and prioritization when a small group or business is concerned. We believe the proposed approach has potential for resolving deficiencies of the conventional voting mechanism, and can be applied to many real-world problems. Its implementation on the Internet is also discussed.

Introduction

Many researchers have studied the problem of combining individual preferences to form a consensus of opinion or compromise. Problems of this nature often appear in resource allocation, project selection, and policy-making. Conventional wisdom regarding public policy-making is grounded in the widespread majority vote mechanism. That is, either a simple or a two-thirds majority vote determines the final decision, and the minority must unconditionally compromise its position. It is a winner-take-all outcome. The losers’ possible strong preferences for the opposite alternative are no longer important, and their cooperation with, and deference to the will of, the majority are expected. While convenient, the current voting system oversimplifies the representation of voter preferences and “drowns out” the true merit of counterarguments. In spite of its fairness, in principle and often in practice, opposing opinions are ignored, and this may be painful to the losers. We wonder if this approach to democracy is ordained by divinity, generated through our biology, or improvised by human rationality. Much attention has been paid by the utility theory researchers to study group decision-making problems (see [1], [2], [3], [4]). However, the absence of a formal, dominating, and widely accepted theory to aggregate cardinal preferences may be a stumbling block that prohibits us from moving beyond the traditional ordinal approach.

Using ballots to solicit the inclination of individuals in a group has been a subject of great interest for nearly 200 years. In Group Choice, Mirkin [5] scanned the diverse horizons of the field. He found that much of the research had focused on the ordinal representation of preferences, and on the problems and pitfalls of the ordinal approach. Barbut [6] constructed examples to illustrate paradoxes of the ordinal approach when voting on three alternatives. Several cases were subsequently shown and demonstrated to be contradictory. This eventually led to the development of the well-known Arrow [7] impossibility theorem for ordinal preferences. The theorem states that if the number of alternatives is greater than two, it is impossible to create a group preference ordering that satisfies four seemingly natural conditions that one would expect to hold. These are non-dictatorship, decisiveness, Pareto optimality (agreement), and independence of irrelevant alternatives.

To remove the contradiction outlined by Arrow, three types of ordinal methods were attempted in the literature: preference scoring, distance-based methods, and statistical methods. These are intended to relax one or the other of the four conditions and, in particular, the fourth one. However, the results are unsatisfactory, at least for addressing the question of the general uniqueness of the outcome regardless of the method used.

In addition to the work of Armstrong et al. [8] and Cook and Seiford [9], Cook and Kress [10] developed a model for aggregating ordinal rankings to express intensity of preference. Mueller [11] and Plott [12] provided an extensive survey for consensus ranking through generalized network formulation. The debate has continued because the roots of impossibility lie in the use of ordinal preferences.

It was once thought that a cardinal approach to aggregating individual preferences is not plausible. MacKay [13] thus writes that pursuing the cardinal approaches is like chasing what cannot be caught. Nevertheless, by considering problems in arms control negotiations, Saaty [14], [15] developed a general theory of measurement based on absolute scales called the Analytic Hierarchy Process (AHP) that does precisely that. AHP provides a method for aggregating individual cardinal preferences into a unique group preference while removing impossibility, as shown by Saaty and Vargas [16]. Because it deals with measurement, AHP facilitates the group process to capture preference intensities of individuals and incorporates them into a final group decision. It ensures the validity of the outcome as it relates to the real world, a question rarely addressed in the ordinal approach.

In the current paper, we illustrate the use of the cardinal approach. It is organized as follows. In Section 2, we discuss the deficiency of the traditional decision-making (voting) system; Section 3 provides the framework for applying the AHP to voting, and for analyzing the sensitivity of the proposed method. In Section 4, we discuss its implementation on the Internet. Summary and conclusions are made in Section 5.

Section snippets

Deficiencies of the traditional yes–no voting system

The traditional voting method requires voters to choose between “yes” and “no” for an alternative. Many regard this (1–0) majority voting method as an unchallengeable law of nature. It is because, thus far, we have not found a way of voting that is more practical and better represents the decision-makers’ true preferences. In this section, we examine the deficiencies of the traditional (1–0) head-count procedure.

First, with a majority vote, individuals are unable to express their true

Applying the AHP to voting

Policy-making requires inputs of eligible individuals or representatives. Our example in this section focuses on the public policy-making issues encountered by a legislative body. The political example in Section 3.1 is meant to give a slightly more serious flavor to the analysis and to draw the attention of readers to matters about which the public is usually concerned. Our hope is to invite a broader and strategic look at our approach. The views expressed here are drawn from newspapers,

Internet and group decision-making

In this section, we examine two potential useful applications of our proposed framework using computers and the Internet. The first is in public policy voting, and the second in business group decision-making.

Conclusions

In this research, we have identified some key shortcomings of traditional majority voting, in which public policy-makers have little or no way to express the intensity of their preferences. We thus developed a voting procedure that is objective, takes into consideration each individual's sentiments, and allows for reasoning based on a structured evaluation framework. The approach is general and relatively easy to understand, and puts voting in a richer human context to match more closely how

Thomas L. Saaty obtained his Ph.D. in mathematics from Yale University. He holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA. He was previously Professor, Wharton School of Business, University of Pennsylvania. Professor Saaty spent seven years at the Arms Control and Disarmament Agency in the US State Department, during which time major arms reduction negotiations were held with the Soviets in Geneva. His current research

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    Thomas L. Saaty obtained his Ph.D. in mathematics from Yale University. He holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA. He was previously Professor, Wharton School of Business, University of Pennsylvania. Professor Saaty spent seven years at the Arms Control and Disarmament Agency in the US State Department, during which time major arms reduction negotiations were held with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution, and synthesis of signals in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored and co-authored more than a dozen books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, and Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. The book is a rich collection of ideas, incorporating research by a growing body of researchers and practitioners, profiles of creative people, projects and products, theory, philosophy, physics and metaphysics…all explained with a liberal dose of humor. He has published more than 300 refereed articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as a consultant to many corporations and governments. In 2005, he was elected to the US National Academy of Engineering.

    Jennifer Shang is Associate Professor, Katz Graduate School of Business, University of Pittsburgh. She received her Ph.D. in Operations Management from the University of Texas at Austin. Her main research interests include multi-criteria decision-making and its application to the design, planning, scheduling, control, and evaluation of production and service operational systems. She has published in various journals, including Management Science, European Journal of Operational Research, IEEE Transactions on Engineering Management, and International Journal of Production Research. She has won the 2005 EMBA Distinguished Teaching Award, and several Excellence in Teaching awards from the MBA/EMBA programs at Katz.

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